4/9g+9=1.9g+15

Solution for 4/9g+9=1.9g+15 equation:

4/9g+9=1.9g+15

We move all terms to the left:

4/9g+9-(1.9g+15)=0


Domain of the equation: 9g!=0

g!=0/9

g!=0

g∈R


We get rid of parentheses

4/9g-1.9g-15+9=0

We multiply all the terms by the denominator


-(1.9g)*9g-15*9g+9*9g+4=0

We add all the numbers together, and all the variables

-(+1.9g)*9g-15*9g+9*9g+4=0

We multiply parentheses

-9g^2-15*9g+9*9g+4=0

Wy multiply elements

-9g^2-135g+81g+4=0

We add all the numbers together, and all the variables

-9g^2-54g+4=0

a = -9; b = -54; c = +4;
Δ = b2-4ac
Δ = -542-4·(-9)·4
Δ = 3060
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{85}}{2*-9}=\frac{54-6\sqrt{85}}{-18}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{85}}{2*-9}=\frac{54+6\sqrt{85}}{-18}
$